MAT 237Y is a multivariable
calculus course.

This year, the course will
present material with more mathematical rigour than before, developing
topics from basic principles and generalizing many subjects.

Together with standard
applications, the course will now include more proofs.

The material of MAT 137Y will
be extended to any number of dimensions, with varying degrees of
difficulty, resulting in very powerful theorems.

The
topics covered include parametric equations and polar coordinates,
vectors and vector functions, basic topology (limits in *n*
dimensions, compact sets, and sets of measure zero), derivatives of
functions of several variables (these will be done starting with the
limit definition), inverse and implicit functions, multiple integrals
(starting at upper and lower sums), and vector calculus (this will be
covered in a very general setting called *k*-cubes, where integrals of
functions with *n* variables will be taken over surfaces of *k*
dimensions).